Few times I faced this issue, while working with Mule 3.8.4. When I Googled I found people are talking about the Mulesoft Enterprise Edition access to download these dependencies for project, but I don't think we need nexus EE access to download these dependencies specially when we are working with Mule 3. Here the problem is something different and your POM might have some additional dependencies which is not available on public nexus repository and due to that this dependency is not getting resolved.
Failed to collect dependencies at com.mulesoft.muleesb:mule-core-ee:jar:3.8.4: Failed to read artifact descriptor for com.mulesoft.muleesb:mule-core-ee:jar:3.8.4: Could not transfer artifact com.mulesoft.muleesb:mule-core-ee:pom:3.8.4 from/to Central (http://repo1.maven.org/maven2/): Failed to transfer file http://repo1.maven.org/maven2/com/mulesoft/muleesb/mule-core-ee/3.8.4/mule-core-ee-3.8.4.pom with status code 501
Resolution:
To resolve this in Mule 3 Anypoint studio, create a new fresh maven project and build it. If this newly created project successfully build then your other project where you are facing this issue will work. Match the project POM.xml file with new project pom and see the dependencies.Example POM.xml file.